Sybirna, A. | bioRxiv Science

bioRxiv2018

Branch-recombinant Gaussian processes for analysis of perturbations in biological time series

MotivationA common class of behaviour encountered in the biological sciences involves branching and recombination. During branching, a statistical process bifurcates resulting in two or more potentially correlated processes that may under-go further branching; the contrary is true during recombination, where two or more statistical processes converge into one. A key objective is to identify the time of this bifurcation (branch time) from time series measurements e.g., comparing a control time series with a perturbed time series. Whilst statistical treatments for the two branch (control versus treatment) case exists, the ability to infer more complex branching structure from time series data remains open. Gaussian processes (GPs) represents an ideal framework for such analysis, allowing for nonlinear regression that includes a rigorous treatment of uncertainty. Currently, however, GP models only exist for two-branch systems. Here we highlight how arbitrarily complex branching processes can be built using the correct composition of covariance functions within a GP framework, thus outlining a general framework for the treatment of branching and recombination in the form of branch-recombinant Gaussian processes (B-RGPs). We first demonstrate the performance of B-RGPs compared to a variety of existing regression approaches, and demonstrate robustness to model misspecification. B-RGPs are then used to investigate the branching patterns of Arabidopsis thaliana gene expression following inoculation with the hemibotrophic bacteria, Pseudomonas syringae DC3000, and a disarmed mutant strain, hrpA. By grouping genes according to the number of branches, we could naturally separate out genes involved in basal immune response from those subverted by the virulent strain, and show enrichment for targets of pathogen protein effectors. Finally, we identify two early branching genes WRKY11 and WRKY17, and showed that groups of genes that branched at similar times to WRKY11/17 were enriched for W-box binding motifs, and overrepresented for genes differentially expressed in WRKY11/17 knockouts, suggesting that branch time could be used for identifying direct and indirect binding targets of key transcription factors. Software is available from: https://github.com/cap76/BranchingGPs.

bioinformatics↗

bioRxiv2017

Nonparametric Bayesian inference of transcriptional branching and recombination identifies regulators of early human germ cell development

During embryonic development, cells undertake a series of fate decisions to form a complete organism comprised of various cell types, epitomising a branching process. A striking example of branching occurs in humans around the time of implantation, when primordial germ cells (PGCs), precursors of sperm and eggs, and somatic lineages are specified. Due to inaccessibility of human embryos at this stage of development, understanding the mechanisms of PGC specification remains difficult. The integrative modelling of single cell transcriptomics data from embryos and appropriate in vitro models should prove to be a useful resource for investigating this system, provided that the cells can be suitably ordered over a developmental axis. Unfortunately, most methods for inferring cell ordering were not designed with structured (time series) data in mind. Although some probabilistic approaches address these limitations by incorporating prior information about the developmental stage (capture time) of the cell, they do not allow the ordering of cells over processes with more than one terminal cell fate. To investigate the mechanisms of PGC specification, we develop a probabilistic pseudotime approach, branch-recombinant Gaussian process latent variable models (B-RGPLVMs), that use an explicit model of transcriptional branching in individual marker genes, allowing the ordering of cells over developmental trajectories with arbitrary numbers of branches. We use first demonstrate the advantage of our approach over existing pseudotime algorithms and subsequently use it to investigate early human development, as primordial germ cells (PGCs) and somatic cells diverge. We identify known master regulators of human PGCs, and predict roles for a variety of signalling pathways, transcription factors, and epigenetic modifiers. By concentrating on the earliest branched signalling events, we identified an antagonistic role for FGF receptor (FGFR) signalling pathway in the acquisition of competence for human PGC fate, and identify putative roles for PRC1 and PRC2 in PGC specification. We experimentally validate our predictions using pharmacological blocking of FGFR or its downstream effectors (MEK, PI3K and JAK), and demonstrate enhanced competency for PGC fate in vitro, whilst small molecule inhibition of the enzymatic component of PRC1/PRC2 reveals reduced capacity of cells to form PGCs in vitro. Thus, B-RGPLVMs represent a powerful and flexible data-driven approach for dissecting the temporal dynamics of cell fate decisions, providing unique insights into the mechanisms of early embryogenesis. Scripts relating to this analysis are available from: https://github.com/cap76/PGCPseudotime

developmental biology↗